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Energy-Levels, Dynamics, and the Maslov Index

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1992)

Abstract

Our aim here is to study periodicity properties of the integral trajectories of the Hamilton vector field of a given pseudodifferential symbol p, lying in energy-level sets of the kind p -1(E), E ∈ [E 1,E 1], with which we shall associate the action integral. This will be done in the next section. In section 11.2 we shall then give a crash introduction to the Maslov index of a periodic trajectory, with the aim of enabling the reader to compute it in the cases of interest for us. In the notes to the chapter we shall also give a rapid overview of the reason why one needs this symplectic invariant, that will systematically appear in Chapter 12.

Keywords

  • Symplectic Form
  • Symmetric Bilinear Form
  • Periodic Trajectory
  • Maslov Index
  • Lagrangian Manifold

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Correspondence to Alberto Parmeggiani .

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Parmeggiani, A. (2010). Energy-Levels, Dynamics, and the Maslov Index. In: Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction. Lecture Notes in Mathematics(), vol 1992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11922-4_11

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